Percentages are most often used to express a variable in terms of that variable's total number (for example, slaves formed 20.2 percent of the total population of Augusta County in 1860). Ratios can be used in cases where the variables being compared represent separate and distinct categories. For example, in order to get a sense of the relative size of each group, one could compute the ratio of students to teachers in the Franklin County public schools in 1850.
The formula for calculating the ratio of variable A to variable B is: (A/B)
Note that, unlike a proportion, a ratio can take on a value greater than one. According to the 1850 census there were 8579 pupils in the Franklin County public schools and 177 teachers. Hence, the ratio of students to teachers was (8579/177) or 48.4. For every teacher, there were, on average, 48.4 students! This can also be written as 48.4:1. Because ratios standardize for population size (we are calculating the number of students per 1 teacher), we can compare the student-teacher ration in Franklin with that of Augusta when a similar figure is computed for that county.
Ratios as computed above are expressed in terms of a base denominator of 1 (the number of students per 1 teacher). However, ratios can be expressed in terms of any base number that you choose by simply multiplying the ratio by that base. Sex ratios, for example, are usually presented in terms of the number of males per 100 females. If we calculate the ratio of white males to white females in Augusta County in 1860 (10880/10667=1.019), and then multiply that number by the base 100 (1.019 * 100=101.9=102), we find that the sex ratio among whites in Augusta County was 102. This indicates that the white male and white female populations in Augusta County were relatively balanced--for every 100 white females there were 102 white males. The sex ratio among Augusta County's slaves, on the other hand, was 203, signifying that there were more than twice as many male slaves as female slaves. Once again, because ratios standardize for population size, we can use this figure to compare the sex ratio of Augusta County's slave population with that for Virginia, or the South as a whole, when similar figures are computed for those regions.
Rates are a special type of ratio. Large base numbers such as 1000 or 100000 are often used to compute rates whenever the use of proportions or percentages would result in very small decimal numbers. Murder rates, for example, are often expressed in terms of the number of murders per 100,000 population.